[R-lang] Re: Concerning glm with contrasts

[Levy, Roger]

Dear Zoe,

On Jul 19, 2010, at 10:28 AM, Zoe Luk wrote:

> Dear R-lang users,
> 
> I am new to the mailing list, and also rather new to R. I have a few questions concerning the results of glm(). 
> 
> I am doing a study comparing the frequencies of different linguistic constructions used in a specific text that is in three languages (Japanese, Chinese, and English). The results I got are the following. 
> 
> 
> Transitive 	Passive	Intransitive	Adjectival	Others	Total
> Japanese	164	9	291	36	8	508
> Chinese	198	3	221	69	17	508
> English	174	31	214	57	32	508
> 
> 536	43	726	162	57	1524
> 
> Chi-square test has a significant result. I intended to do further analysis to see if there is any difference among the languages, so i did the following:
> 
> > glm.out4<-glm(freq~language*constructions, data=comps2.data, family=poisson, contrasts=list(language=contrastml, constructions=contrastmc))

The first question I'd like to ask is why you're using a Poisson model to analyze your data.  I see that the marginal totals for each language are the same at 508.  Were these marginal totals under your control (e.g., did you count in each text until you got 508), or are these totals something you want your model to account for?  A Poisson model devotes parameters to accounting for the marginal totals. If instead you're thinking that the language is an "independent variable" and the construction type is a "dependent variable", then analyzing the data with multinomial logistic regression might be more appropriate.  (Now, there *are* legitimate uses of Poisson models as surrogates for multinomial logistic regression, but using them in surrogates in this way affects how you interpret the model parameters -- see below.)

> > summary(glm.out4)
> 
> Call:
> glm(formula = freq ~ language * constructions, family = poisson, 
>     data = comps2.data, contrasts = list(language = contrastml, 
>         constructions = contrastmc))
> 
> Deviance Residuals: 
>  [1]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
> 
> Coefficients:
>                          Estimate Std. Error z value Pr(>|z|)    
> (Intercept)               3.93111    0.05890  66.746  < 2e-16 ***
> language1                 0.20443    0.08435   2.424 0.015363 *  
> language2                 0.16064    0.09497   1.692 0.090740 .  
> constructions1           -1.25129    0.06779 -18.459  < 2e-16 ***
> constructions2            1.68783    0.18775   8.990  < 2e-16 ***
> constructions3           -0.01655    0.08647  -0.191 0.848205    
> constructions4            1.12805    0.13321   8.468  < 2e-16 ***
> language1:constructions1  0.12190    0.09726   1.253 0.210090    
> language2:constructions1  0.26651    0.10562   2.523 0.011625 *  
> language1:constructions2  0.15838    0.24722   0.641 0.521744    
> language2:constructions2 -0.98403    0.32782  -3.002 0.002684 ** 
> language1:constructions3 -0.15971    0.12915  -1.237 0.216218    
> language2:constructions3  0.44708    0.12620   3.543 0.000396 ***
> language1:constructions4 -0.51918    0.21538  -2.411 0.015931 *  
> language2:constructions4  0.19079    0.18724   1.019 0.308207    
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> 
> (Dispersion parameter for poisson family taken to be 1)
> 
>     Null deviance:  1.3744e+03  on 14  degrees of freedom
> Residual deviance: -3.1086e-15  on  0  degrees of freedom
> AIC: 116.66
> 
> Number of Fisher Scoring iterations: 3
> 
> > contrasts(language)
>          [,1] [,2]
> Chinese     0   -1
> English     1    1
> Japanese   -1    0
> > contrasts(constructions)
>              [,1] [,2] [,3] [,4]
> Adjectival      0    0   -1    0
> Intransitive    1    1    1    1
> Others          0    0    0   -1
> Passive         0   -1    0    0
> Transitive     -1    0    0    0
> 
> So my questions are:
> (1) I am not sure how to interpret these results. Since language1 shows a significance difference, does it mean that "English and Japanese are significantly different in terms of the distribution of the different constructions used"? 

No -- since you're using Poisson regression, the language1 variable more or less models the relative frequency of English observations to Japanese observations.

If you were to double the number of observations in each Japanese cell, the biggest change in your model would be that the language1 parameter would decrease.  (The intercept and the language2 parameter would also adjust by smaller amounts, in compensation.)  The constructions and language:constructions parameters would stay the same

> (2) Does the "intercept" represent anything at all? If yes, what does it represent in this case?

It probably not anything you're interested in.  Because you're using true contrasts (i.e. each column in your contrast matrices sums to zero), the intercept is more or less modeling the total number of observations in your dataset (keep in mind that Poisson regression is trying to model cell counts, not proportions).

If you were to double the counts of all cells in your dataset, the intercept would increase by a constant factor -- log(2) -- and the rest of the model would stay the same.

> (3) If I want to test whether English uses passive significantly more than Japanese, and Japanese uses intransitive significantly more than English, how should I modify the contrasts/commands?

Let's call the passive question 3a, and the intransitive question 3b.  Answering these question depends on the answers to a couple of other questions:

* How, if at all, are the Chinese data relevant to either 3a or 3b?

* How, if at all, are the distinctions among adjectival, intransitive, transitive, and "other" relevant to 3a?

* How, if at all, are the distinctions among adjectival, passive, transitive, and "other" relevant to 3b?

If the answer to all three questions is "irrelevant", you might just consider doing very simple chi-squared or Fisher's exact tests on 2x2 representations of the Japanese and English as (a) passive and non-passive counts, and (b) intransitive and non-intransitive counts.

Also, I'd recommend Maureen Gillespie's coding tutorial as background reading:

http://go2.wordpress.com/?id=725X1342&site=hlplab.wordpress.com&url=http%3A%2F%2Fhlplab.files.wordpress.com%2F2010%2F05%2Fcodingtutorial.pdf&sref=http%3A%2F%2Fhlplab.wordpress.com%2F2010%2F05%2F10%2Fmini-womm-montreal-slides-now-available%2F

Best

Roger

--

Roger Levy                      Email: rlevy@ling.ucsd.edu
Assistant Professor             Phone: 858-534-7219
Department of Linguistics       Fax:   858-534-4789
UC San Diego                    Web:   http://ling.ucsd.edu/~rlevy